Distributed load management in anycast-based CDNs
01 Sep 2015-pp 74-82
TL;DR: In this paper, the authors propose an analytical framework to formulate and solve the load-management problem in anycast addressing, which offers simplicity of design and high availability of service at the cost of partial loss of routing control.
Abstract: Anycast is an internet addressing protocol where multiple hosts share the same IP-address. A popular architecture for modern Content Distribution Networks (CDNs) for geo-replicated HTTP-services consists of multiple layers of proxy nodes for service and co-located DNS-servers for load-balancing on different proxies. Both the proxies and the DNS-servers use anycast addressing, which offers simplicity of design and high availability of service at the cost of partial loss of routing control. Due to the very nature of anycast, load-management actions by a co-located DNS-server also affects loads at nearby proxies in the network. This makes the problem of distributed load management highly challenging. In this paper, we propose an analytical framework to formulate and solve the load-management problem in this context. We consider two distinct algorithms. In the first half of the paper, we pose the load-management problem as a convex optimization problem. Following a dual decomposition technique, we propose a fully-distributed load-management algorithm by introducing FastControl packets. This algorithm utilizes the underlying anycast mechanism itself to enable effective coordination among the nodes, thus obviating the need for any external control channel. In the second half of the paper, we consider an alternative greedy load-management heuristic, currently in production in a major commercial CDN. We study its dynamical characteristics and analytically identify its operational and stability properties. Finally, we critically evaluate both the algorithms and explore their optimality-vs-complexity trade-off using trace-driven simulations.
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TL;DR: The Universal Max-Weight (UMW) as discussed by the authors policy is the first known throughput-optimal policy of such versatility in the context of generalized network flow problems, which is derived by relaxing the precedence constraints associated with multi-hop routing and then solving a min-cost routing and max-weight scheduling problem on a virtual network of queues.
Abstract: We consider the problem of throughput-optimal packet dissemination, in the presence of an arbitrary mix of unicast, broadcast, multicast, and anycast traffic, in an arbitrary wireless network. We propose an online dynamic policy, called Universal Max-Weight (UMW), which solves the problem efficiently. To the best of our knowledge, UMW is the first known throughput-optimal policy of such versatility in the context of generalized network flow problems. Conceptually, the UMW policy is derived by relaxing the precedence constraints associated with multi-hop routing and then solving a min-cost routing and max-weight scheduling problem on a virtual network of queues . When specialized to the unicast setting, the UMW policy yields a throughput-optimal cycle-free routing and link scheduling policy. This is in contrast with the well-known throughput-optimal back-pressure (BP) policy which allows for packet cycling, resulting in excessive latency. Extensive simulation results show that the proposed UMW policy incurs a substantially smaller delay as compared with the BP policy. The proof of throughput-optimality of the UMW policy combines ideas from the stochastic Lyapunov theory with a sample path argument from adversarial queueing theory and may be of independent theoretical interest.
28 citations
01 May 2017
TL;DR: The proof of throughput-optimality of the UMW policy combines techniques from stochastic Lyapunov theory with a sample path argument from adversarial queueing theory and may be of independent theoretical interest.
Abstract: We consider the problem of throughput-optimal packet dissemination, in the presence of an arbitrary mix of unicast, broadcast, multicast and anycast traffic, in a general wireless network. We propose an online dynamic policy, called Universal Max-Weight (UMW), which solves the above problem efficiently. To the best of our knowledge, UMW is the first throughput-optimal algorithm of such versatility in the context of generalized network flow problems. Conceptually, the UMW policy is derived by relaxing the precedence constraints associated with multi-hop routing, and then solving a min-cost routing and max-weight scheduling problem on a virtual network of queues. When specialized to the unicast setting, the UMW policy yields a throughput-optimal cycle-free routing and link scheduling policy. This is in contrast to the well-known throughput-optimal BackPressure (BP) policy which allows for packet cycling, resulting in excessive delay. Extensive simulation results show that the proposed policy incurs a substantially lower delay as compared to the BP policy. The proof of throughput-optimality of the UMW policy combines techniques from stochastic Lyapunov theory with a sample path argument from adversarial queueing theory and may be of independent theoretical interest.
21 citations
Dissertation•
13 Jan 2018
TL;DR: This dissertation aims to provide a history of web exceptionalism from 1989 to 2002, a period chosen in order to explore its roots as well as specific cases up to and including the year in which descriptions of “Web 2.0” began to circulate.
Abstract: Put your abstract or summary here, if your university requires it.
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Book•
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TL;DR: Undergraduate and graduate classes in computer networks and wireless communications; undergraduate classes in discrete mathematics, data structures, operating systems and programming languages.
Abstract: Undergraduate and graduate classes in computer networks and wireless communications; undergraduate classes in discrete mathematics, data structures, operating systems and programming languages. Also give lectures to both undergraduate-and graduate-level network classes and mentor undergraduate and graduate students for class projects.
6,991 citations
Book•
01 Jan 1964
TL;DR: The real and complex number system as discussed by the authors is a real number system where the real number is defined by a real function and the complex number is represented by a complex field of functions.
Abstract: Chapter 1: The Real and Complex Number Systems Introduction Ordered Sets Fields The Real Field The Extended Real Number System The Complex Field Euclidean Spaces Appendix Exercises Chapter 2: Basic Topology Finite, Countable, and Uncountable Sets Metric Spaces Compact Sets Perfect Sets Connected Sets Exercises Chapter 3: Numerical Sequences and Series Convergent Sequences Subsequences Cauchy Sequences Upper and Lower Limits Some Special Sequences Series Series of Nonnegative Terms The Number e The Root and Ratio Tests Power Series Summation by Parts Absolute Convergence Addition and Multiplication of Series Rearrangements Exercises Chapter 4: Continuity Limits of Functions Continuous Functions Continuity and Compactness Continuity and Connectedness Discontinuities Monotonic Functions Infinite Limits and Limits at Infinity Exercises Chapter 5: Differentiation The Derivative of a Real Function Mean Value Theorems The Continuity of Derivatives L'Hospital's Rule Derivatives of Higher-Order Taylor's Theorem Differentiation of Vector-valued Functions Exercises Chapter 6: The Riemann-Stieltjes Integral Definition and Existence of the Integral Properties of the Integral Integration and Differentiation Integration of Vector-valued Functions Rectifiable Curves Exercises Chapter 7: Sequences and Series of Functions Discussion of Main Problem Uniform Convergence Uniform Convergence and Continuity Uniform Convergence and Integration Uniform Convergence and Differentiation Equicontinuous Families of Functions The Stone-Weierstrass Theorem Exercises Chapter 8: Some Special Functions Power Series The Exponential and Logarithmic Functions The Trigonometric Functions The Algebraic Completeness of the Complex Field Fourier Series The Gamma Function Exercises Chapter 9: Functions of Several Variables Linear Transformations Differentiation The Contraction Principle The Inverse Function Theorem The Implicit Function Theorem The Rank Theorem Determinants Derivatives of Higher Order Differentiation of Integrals Exercises Chapter 10: Integration of Differential Forms Integration Primitive Mappings Partitions of Unity Change of Variables Differential Forms Simplexes and Chains Stokes' Theorem Closed Forms and Exact Forms Vector Analysis Exercises Chapter 11: The Lebesgue Theory Set Functions Construction of the Lebesgue Measure Measure Spaces Measurable Functions Simple Functions Integration Comparison with the Riemann Integral Integration of Complex Functions Functions of Class L2 Exercises Bibliography List of Special Symbols Index
6,681 citations
01 Jan 1997
TL;DR: This paper addresses the issues of charging, rate control and routing for a communication network carrying elastic traffic, such as an ATM network offering an available bit rate service, from which max-min fairness of rates emerges as a limiting special case.
Abstract: This paper addresses the issues of charging, rate control and routing for a communication network carrying elastic traffic, such as an ATM network offering an available bit rate service. A model is described from which max-min fairness of rates emerges as a limiting special case; more generally, the charges users are prepared to pay influence their allocated rates. In the preferred version of the model, a user chooses the charge per unit time that the user will pay; thereafter the user's rate is determined by the network according to a proportional fairness criterion applied to the rate per unit charge. A system optimum is achieved when users' choices of charges and the network's choice of allocated rates are in equilibrium.
3,067 citations
TL;DR: This book discusses Chaos, Fractals, and Dynamics, and the Importance of Being Nonlinear in a Dynamical View of the World, which aims to clarify the role of Chaos in the world the authors live in.
Abstract: Preface 1. Overview 1.0 Chaos, Fractals, and Dynamics 1.1 Capsule History of Dynamics 1.2 The Importance of Being Nonlinear 1.3 A Dynamical View of the World PART I. ONE-DIMENSIONAL FLOWS 2. Flows on the Line 2.0 Introduction 2.1 A Geometric Way of Thinking 2.2 Fixed Points and Stability 2.3 Population Growth 2.4 Linear Stability Analysis 2.5 Existence and Uniqueness 2.6 Impossibility of Oscillations 2.7 Potentials 2.8 Solving Equations on the Computer Exercises 3. Bifurcations 3.0 Introduction 3.1 Saddle-Node Bifurcation 3.2 Transcritical Bifurcation 3.3 Laser Threshold 3.4 Pitchfork Bifurcation 3.5 Overdamped Bead on a Rotating Hoop 3.6 Imperfect Bifurcations and Catastrophes 3.7 Insect Outbreak Exercises 4. Flows on the Circle 4.0 Introduction 4.1 Examples and Definitions 4.2 Uniform Oscillator 4.3 Nonuniform Oscillator 4.4 Overdamped Pendulum 4.5 Fireflies 4.6 Superconducting Josephson Junctions Exercises PART II. TWO-DIMENSIONAL FLOWS 5. Linear Systems 5.0 Introduction 5.1 Definitions and Examples 5.2 Classification of Linear Systems 5.3 Love Affairs Exercises 6. Phase Plane 6.0 Introduction 6.1 Phase Portraits 6.2 Existence, Uniqueness, and Topological Consequences 6.3 Fixed Points and Linearization 6.4 Rabbits versus Sheep 6.5 Conservative Systems 6.6 Reversible Systems 6.7 Pendulum 6.8 Index Theory Exercises 7. Limit Cycles 7.0 Introduction 7.1 Examples 7.2 Ruling Out Closed Orbits 7.3 Poincare-Bendixson Theorem 7.4 Lienard Systems 7.5 Relaxation Oscillators 7.6 Weakly Nonlinear Oscillators Exercises 8. Bifurcations Revisited 8.0 Introduction 8.1 Saddle-Node, Transcritical, and Pitchfork Bifurcations 8.2 Hopf Bifurcations 8.3 Oscillating Chemical Reactions 8.4 Global Bifurcations of Cycles 8.5 Hysteresis in the Driven Pendulum and Josephson Junction 8.6 Coupled Oscillators and Quasiperiodicity 8.7 Poincare Maps Exercises PART III. CHAOS 9. Lorenz Equations 9.0 Introduction 9.1 A Chaotic Waterwheel 9.2 Simple Properties of the Lorenz Equations 9.3 Chaos on a Strange Attractor 9.4 Lorenz Map 9.5 Exploring Parameter Space 9.6 Using Chaos to Send Secret Messages Exercises 10. One-Dimensional Maps 10.0 Introduction 10.1 Fixed Points and Cobwebs 10.2 Logistic Map: Numerics 10.3 Logistic Map: Analysis 10.4 Periodic Windows 10.5 Liapunov Exponent 10.6 Universality and Experiments 10.7 Renormalization Exercises 11. Fractals 11.0 Introduction 11.1 Countable and Uncountable Sets 11.2 Cantor Set 11.3 Dimension of Self-Similar Fractals 11.4 Box Dimension 11.5 Pointwise and Correlation Dimensions Exercises 12. Strange Attractors 12.0 Introductions 12.1 The Simplest Examples 12.2 Henon Map 12.3 Rossler System 12.4 Chemical Chaos and Attractor Reconstruction 12.5 Forced Double-Well Oscillator Exercises Answers to Selected Exercises References Author Index Subject Index
2,949 citations